3.2 Description of capacity management related problems 28
order stream also needs to be respected when deciding about the applied resources. These aspects lead to a complex system configuration problem, namely to determine the set of applied assembly resources, and assign the products to these resource sets (Figure 3.5). In the configuration problem, three different system types s ∈ S are considered: reconfigurable (s = r), flexible (s=f) and dedicated (s=d) systems. The main objective is to minimize the total cost incurs on a certain time horizonU. This cost is the sum of investments in different production resources Λsu, as well as the production rate related expenses Γs, characterizing the operation of system s. Additional costs χ of assigning the products to a new system type, and depreciation of the resources Ψ are also considered.
These costs can be minimized by making right decisions in each time periodu∈U, assigning the products to one of the three system types. These actions are naturally accompanied by system configuration decisions, adjusting the production capacities to the customer order stream. In each planning period u∈U, all products p∈P need to be assigned to one system type s∈S.
Besides, the investment costs with the amount of additional modules nj from each type j ∈J also need to be determined (Figure 3.5). These investment and system configuration decisions are taken on a strategic level, considering volume forecastsfpuand a relatively long time horizon (typically some years). Additional complexity in the problem is introduced by the order volumes that change over time, and related forecasts are uncertain.
Tasks
Assign the product to resources over time
Define the system configuration over time Challenges
Forecast volumes are uncertain
Order volumes change over time
Costs are specific to resources
The applied system configuration, the product-resource assignments and the production and investment costs are interdependent
Market/Customers
Product-resource assignment and system configuration Product portfolio
Order volumes
?
Invesment costs Operation costs
Forecast volumes
Prod n Prod
1 Prod
2 Prod
3
Dedicated resources
Reconfigurable resources
Flexible resources
Figure 3.5. Illustration of the analyzed product-assembly system assignment and system configuration problem, highlighting the special tasks and challenges.
Constraints
Although it would be simple to assign each product to dedicated resources that will certainly provide the target production rate, this strategy would lead to excess costs due to the facts summarized in Section 3.1.2. When configuring the system, various constraints need to be con-sidered, e.g. the available shop-floor space mmax and the available human workforce hmax as technological constraints. Besides, different cost factors are considered: the purchase cost of the modulesmprices , the cost of setupscsetand reconfigurationscrec, the salaries of the operatorscopr and the operation costs copn of the modules. In the considered problem, modules of different system typesscan have different level of automationmauts , influencing the total time required to assemble a certain product in a selected system type. The space requirementmspaces , and also the purchase costmprices of modules depend on the system type. Concluding the above thoughts, the system configuration problem is solved by utilizing the advantages offered by the combination
29 3.2 Description of capacity management related problems
of the different resource types, and assigning the products to proper resources according to mul-tiple criteria. Applying an optimization model, the cost-optimal system configuration —capable of providing the desired production rate— is to be obtained in each decision period.
3.2.2 Production planning problem in modular assembly systems
In case of the dedicated resources, calculation of the investment costs is quite straightforward, as the amount of modules to be purchased is given for each product. As highlighted earlier, flexible and reconfigurable systems are characterized with dynamic operation, which means that resources are shared among different products, therefore, the required number of modules is not only product-, but also operation-dependent. Conclusively, the performance of modular reconfig-urable assembly systems and incurring costs are strongly influenced by the system configuration, and also by the applied planning and scheduling policy (Gyulai et al., 2014b, 2012). As intro-duced in Section 3.1.2, volume-related operational costs in these dynamic systems are also rather complex to estimate, as they can be operated economically if several product types (family) are assigned.
It is also essential that strategic decisions influence the execution of tactical-level produc-tion plans, hence the link between these levels is of crucial importance. The assembly system configuration together with the product-assembly system assignments and the available capac-ities constrain decisions when planning the production, therefore, planning aspects need to be considered when configuring system. Production planning decisions in the analyzed capacity management problem are responsible for calculating the production lot sizes, with the objective of minimizing the total production costs on a medium-term, discrete time horizon. In the con-sidered production planning problem, the objective is to determine the lot sizesxnt by matching the available internal capacities (human and machine) with the customer demands. The plan-ning horizon T is divided into time buckets t ∈ T with equal length tw, and a given set of orders n∈N corresponding to productsp∈P need to be completed. To perform the assembly operations, j ∈ J different module types are available, and each type is dedicated to a single operation type. The amount of modules from each type j is limited by the resource poolravailj .
Based on the above assumptions, the production planning problem is specified as it follows.
The production lot executions are to be determined with the binary decision variables xnt, specifying if order n is executed in periodt. Each order n is associated with a product type p specified by pn, the order volume qn and a due datetdn. The parameterschn and cln respectively express that both early and late execution of the orders are penalized with extra costs, according to the following formula:
cnt =
chnqn(tdn−t) ift < tdn, clnqn(t−tdn) otherwise.
(3.1) The products are characterized with their total manual processing time tprocp , setup time tsetp and the number of modules rjp required by type j. The objective of planning is to minimize the overall costs realized over the horizon, including the following factors: operator copr, setup cset, deviation cnt and operation copn costs. The essence of assembly technology is that human resources can be flexibly adjusted to change the throughput of the lines. Therefore, production planning is performed together with capacity planning by calculating the allocated headcount of operators in each period.
3.3 Product-based line assignment 30